A family (also described as a familial connection) was a relationship between people by genetics, marriage, adoption, or an especially strong friendship. Those in a family were typically described as relatives; those that lived prior to an individual were known as ancestors, while those that lived after an individual were known as descendants.

In 2287, Leonard McCoy wondered aloud why he, James T. Kirk, and Spock spent time together on shore leave, despite serving together on the Enterprise-A, and especially given their mutual antagonism of each other, remarking that other people had families (who they spent time with). Kirk agreed that other people did, but not them. After Kirk later referred to Spock as his brother, whom he lost but had later regained, McCoy noted the inconsistency between that comment and Kirk's earlier one about them not having families. Kirk admitted that he had been wrong about that (i.e. they did have families - each other.) (Star Trek V: The Final Frontier)

"I know who you are.""Then, you have the advantage.""You're my nephew, Jean-Luc. From the starship Enterprise.""Then you must be my uncle Rene.""I'm not your uncle. It's the other way around.""Too bad. I rather enjoyed the idea."

When Dobara, the wife of Nikolai Rozhenko, chatted with Worf, she begged him to make amends with his brother, because, she wanted Worf to consider himself her brother as well, because he was "going to be the uncle of my child." (TNG: "Homeward")